Em anuros, o canto de anúncio é aquele emitido por machos para atrair fêmeas ou repelir machos competidores na paisagem acústica (Wells 1977; Duellman & Trueb 1986). A maioria das espécies de anuros apresentam comportamento noturno e portanto são altamente dependentes do canto para se reproduzirem. Contudo, na espécie Hylodes asper (Anura: Hylodidae) os machos apresentam comportamento diurno, sedentário e esperam até as fêmeas chegarem nos sítios reprodutivos, onde cantam em superfícies de rochas próximas a águas lóticas (i.e. rios de correnteza intensa ou cachoeiras; Heyer et al. 1990; Haddad & Giaretta 1999). Devido à disponibilidade de luz e ao ruído de fundo das correntezas, sinais visuais podem ser apresentados concomitantemente aos sinais acústicos para maximizar a transmissão de informação entre o macho emissor e as fêmeas ou machos receptores (Hödl et al. 1997). Embora a maioria dos estudos utilize aspectos temporais (e.g. taxa de cantos) ou espectrais (i.e. o quão agudo ou grave o canto é) como variáveis respostas de modelos (e.g. Gingras et al. 2013; Goutte et al. 2016), o tempo em que as fêmeas demoram para chegar nos sítios reprodutivos e iniciarem o amplexo é pouco estudado.
Existem sinais multimodais compostos por características morfológicas, acústicas e visuais que são consideradas mais atrativas pelas fêmeas e podem explicar o tempo até sua chegada e início do amplexo. Por exemplo, uma possível preditora acústica é a frequência dominante do canto (DF: a banda com maior concentração de energia no espectro; Köhler et al. 2017), no qual cantos mais graves são considerados mais atrativos e talvez reduzam o tempo até o início do amplexo, pois machos com canto mais grave geralmente tem cordas vocais mais espessas e compridas (McClelland et al. 1996), o que geralmente é um sinal honesto que informa o tamanho corporal do macho (Wells 2007; Köhler et al. 2017). Contudo, existem machos que mentem! Machos mentirosos são comuns em algumas espécies, os quais conseguem modular a frequência do canto (i.e. deixar mais grave por relaxamento dos músculos da cartilagem aritenóide; Martin 1971; Schmid 1979; Ryan 1988). Por isso, incluir o tamanho corporal como uma variável preditora é uma forma de avaliar a honestidade da frequência. Por fim, machos da espécie Hylodes asper às vezes cantam ao mesmo tempo em que apresentam um display visual chamado foot-flagging, no qual esticam as pernas para chamarem atenção das fêmeas visualmente devido ao barulho das corredeiras que podem reduzir as chances de serem escutados pelas fêmeas (Heyer et al. 1990; Haddad & Giaretta 1999). Portanto, uma última hipótese é que uma taxa de foot-flagging alta reduza o tempo até as fêmeas iniciarem o amplexo.
O objetivo geral desse trabalho é responder como sinais multi-modais influenciam o tempo até o início do amplexo em Hylodes asper. Os objetivos específicos são entender:
Embora dados das nossas variáveis preditoras sejam mais acessíveis na literatura, dados da nossa variável resposta (tempo de espera da fêmea até início da cópula) são escassos. Isso ocorre pois é extremamente custoso ao biólogo de campo tentar localizar uma fêmea de anuro próxima dos machos já que elas não cantam e raramente são vistas na natureza. Portanto, optamos pelo uso de dados simulados.
As nossas variáveis preditoras teóricas são frequência do canto, tamanho corporal e display de foot-flagging. Contudo, precisamos operacionalizar essas variáveis. Utilizamos as seguintes variáveis preditoras operacionais:
Frequência dominante (DF: medida em Hz), definida como a frequência no espectro harmônico com maior concentração de energia que é percebida pelo ouvido humano como o quão grave ou agudo os sons são (Köhler et al. 2017);
Comprimento rostro-cloacal (SVL: snout-vent length, medida em mm), o qual é amplamente usado como aproximação do tamanho corporal pois mede o comprimento da extremedidade anterior do focinho até a extremidade posterior da cloaca (Duellman 1970);
Taxa de foot-flagging (medida em número de eventos/minuto).
Para Hylodes asper, Haddad & Giaretta (1999) reportaram que a DF se encontra no terceiro harmônico entre 5000 a 6500 Hz, com valor de midpoint ([máx - min] / 2) igual a 5750 Hz. Heyer et al. (1990) reportaram que os machos apresentam um SVL médio de 40.5 mm (39.4-42.3 mm). Já a taxa de foot-flagging não foi reportada por unidade de tempo em nenhum destes trabalhos, mas é possível estimar através de vídeos disponíveis no YouTube (~10 a cada 5 min). Utilizamos estes valores como referência das características dos machos simulados na função ‘saposim’.
source("R/funcoes_auxiliares.R")
source("R/saposim.R")
A cada simução é criada uma nova matriz de espaco de
area linhas e area colunas. Em seguida, são
sorteadas as posições dos nmacho daquela simulação. A
frequência dominante do canto freq (DF: Hz), taxa de
foot-flagging foot (número de eventos de
foot-flagging/minuto) e tamanho corporal tama
(SVL: mm) de cada um dos machos é simulada. Estas caracteristicas são
sorteadas a partir de uma distribuição (normal, poisson e normal para
DF, taxa de foot-flagging e SVL, respectivamente) e, em
seguida, padronizadas pela função padroniza. Os valores
padronizados aparecem no output como freqpad,
footpad e tamapad. É esperado que machos mais
próximos à cachoeira tenham menor tamanho corporal (SVL menor) e
vocalizem em frequencias mais agudas (DF maior) e portanto tenham, em
média, probabilidade menor de atrair fêmeas. No entanto, é esperado que
esses machos tenham também maior taxa de foot-flagging, o que
pode contra-balancear essa esperança. Apesar de estes valores serem
correlacionados, as características do macho são sorteadas
independentemente de uma distribuição aleatória.
Todos os machos ficam parados, sem mudarem os sítios reprodutivos, pois eles são altamente territoriais. Portanto, apenas a fêmea se locomove.
A probabilidade de seleção do macho é então calculada através de uma regressão logistica, \[P = \frac{e^{exprlin}}{1+e^{exprlin}}\] com expressão linear de fórmula: \(exprlin = a \times tamanho + b \times taxafootflag + c \times DF\) e intercepto igual à média da expressão linear.
Uma cédula vazia é então sorteada para a fêmea ocupar, e esta escolhe
um macho para copular com probabilidade prob. A distância
distf entre a fêmea e o macho escolhido é calculada pela
função dist. A fêmea e o macho são considerados ocupados
até o final da simulação e são retirados do espaco. A
simulação se repete com nfemea = nmacho. O tempo total
ttot para o macho ser escolhido também é guardado, sendo
definido como a soma de todas distf anteriores na mesma
simulação. A função de simulação de sapos, saposim se
encontra na íntegra no arquivo “R/saposim.R”.
Além do efeito das características dos sapos, decidimos também
investigar se a variação na area da cachoeira é relevante
para o tempo até o início do amplexo. Como resultado, apresentamos então
quatro simulações:
sim_Avar - dimensões da cachoeira (area)
sorteada de uma distribuição uniforme entre 10 e 100 (arredondada para
números inteiros).sim_Afix10 - dimensões da cachoeira (area)
fixa em 10.sim_Afix50 - dimensões da cachoeira (area)
fixa em 50.sim_Afix100 - dimensões da cachoeira
(area) fixa em 100.Em ambas as simulações foram mantidas os valores padrão:
nsim = 1000vecarea = round(runif(nsim, 10, 100), 0)vecnmacho = vecareacffreq = -1.05cftama = 0.5cffoot = 0.8O código das simulações está no documento “R/simula_dados.R”. Como
nsim é grande e leva alguns minutos, salvamos o resultado
das simulações como arquivos R.data.
load("data/sim_Avar.Rdata")
load("data/sim_Afix10.Rdata")
load("data/sim_Afix50.Rdata")
load("data/sim_Afix100.Rdata")
Para exemplificar, as primeiras linhas do dataset simulado com área variada:
head(sim_Avar)
## machoid dcach foot freq tama footpad freqpad tamapad
## 1 m11 2 10 5451.175 37.75195 1.61327113 -1.2945480 -1.5740926
## 2 m8 0 9 5471.879 38.90818 1.29416256 -1.1686849 -0.8205330
## 3 m1 14 5 5620.209 43.37799 0.01772825 -0.2669635 2.0926267
## 4 m18 16 2 5912.848 41.34550 -0.93959747 1.5120276 0.7679693
## 5 m13 15 3 5706.639 37.99239 -0.62048890 0.2584560 -1.4173923
## 6 m14 6 5 5498.009 40.90733 0.01772825 -1.0098380 0.4823968
## exprlin prob distf ttot nsim femea area femeasim
## 1 1.862846 0.8656283 17.117243 17.11724 sim1 f01 18 f01_sim1
## 2 1.852183 0.8643832 16.278821 33.39606 sim1 f02 18 f02_sim1
## 3 1.340808 0.7926227 4.123106 37.51917 sim1 f03 18 f03_sim1
## 4 -1.955322 0.1239742 7.280110 44.79928 sim1 f04 18 f04_sim1
## 5 -1.476466 0.1859618 10.295630 55.09491 sim1 f05 18 f05_sim1
## 6 1.315711 0.7884672 10.770330 65.86524 sim1 f06 18 f06_sim1
summary(sim_Avar)
## machoid dcach foot freq
## Length:53691 Min. : 0.00 Min. : 0.000 Min. :4907
## Class :character 1st Qu.:13.00 1st Qu.: 0.000 1st Qu.:5564
## Mode :character Median :29.00 Median : 0.000 Median :5698
## Mean :32.74 Mean : 1.931 Mean :5699
## 3rd Qu.:49.00 3rd Qu.: 3.000 3rd Qu.:5834
## Max. :99.00 Max. :21.000 Max. :6490
## tama footpad freqpad tamapad
## Min. :31.48 Min. :-2.2900 Min. :-4.043686 Min. :-4.432309
## 1st Qu.:39.05 1st Qu.:-0.5047 1st Qu.:-0.675515 1st Qu.:-0.667948
## Median :40.39 Median :-0.4262 Median :-0.003579 Median : 0.001529
## Mean :40.39 Mean : 0.0000 Mean : 0.000000 Mean : 0.000000
## 3rd Qu.:41.75 3rd Qu.: 0.1149 3rd Qu.: 0.673799 3rd Qu.: 0.672612
## Max. :48.64 Max. : 6.2031 Max. : 3.833402 Max. : 4.099560
## exprlin prob distf ttot
## Min. :-4.74942 Min. :0.008582 Min. : 1.00 Min. : 1.0
## 1st Qu.:-0.94489 1st Qu.:0.279913 1st Qu.: 17.46 1st Qu.: 363.7
## Median :-0.07159 Median :0.482109 Median : 31.32 Median : 983.4
## Mean : 0.00000 Mean :0.493864 Mean : 34.74 Mean :1328.4
## 3rd Qu.: 0.85729 3rd Qu.:0.702094 3rd Qu.: 48.38 3rd Qu.:2017.4
## Max. : 6.97070 Max. :0.999062 Max. :128.76 Max. :5594.0
## nsim femea area femeasim
## Length:53691 Length:53691 Min. : 10.00 Length:53691
## Class :character Class :character 1st Qu.: 48.00 Class :character
## Mode :character Mode :character Median : 71.00 Mode :character
## Mean : 66.48
## 3rd Qu.: 86.00
## Max. :100.00
summary(sim_Afix10)
## machoid dcach foot freq
## Length:10000 Min. :0.0 Min. : 0.000 Min. :4946
## Class :character 1st Qu.:2.0 1st Qu.: 5.000 1st Qu.:5568
## Mode :character Median :4.5 Median : 8.000 Median :5701
## Mean :4.5 Mean : 7.754 Mean :5701
## 3rd Qu.:7.0 3rd Qu.:10.000 3rd Qu.:5837
## Max. :9.0 Max. :23.000 Max. :6503
## tama footpad freqpad tamapad
## Min. :31.51 Min. :-2.57214 Min. :-2.666979 Min. :-2.663643
## 1st Qu.:39.02 1st Qu.:-0.70871 1st Qu.:-0.683235 1st Qu.:-0.686343
## Median :40.40 Median :-0.07459 Median : 0.007767 Median : 0.005384
## Mean :40.38 Mean : 0.00000 Mean : 0.000000 Mean : 0.000000
## 3rd Qu.:41.75 3rd Qu.: 0.64670 3rd Qu.: 0.701655 3rd Qu.: 0.687488
## Max. :48.26 Max. : 2.67226 Max. : 2.592584 Max. : 2.626311
## exprlin prob distf ttot
## Min. :-4.22456 Min. :0.01442 Min. : 1.000 Min. : 1.00
## 1st Qu.:-0.93198 1st Qu.:0.28252 1st Qu.: 3.162 1st Qu.:15.31
## Median :-0.00813 Median :0.49797 Median : 5.099 Median :28.58
## Mean : 0.00000 Mean :0.49915 Mean : 5.265 Mean :29.09
## 3rd Qu.: 0.93679 3rd Qu.:0.71845 3rd Qu.: 7.071 3rd Qu.:41.76
## Max. : 4.60261 Max. :0.99007 Max. :12.728 Max. :79.22
## nsim femea area femeasim
## Length:10000 Length:10000 Min. :10 Length:10000
## Class :character Class :character 1st Qu.:10 Class :character
## Mode :character Mode :character Median :10 Mode :character
## Mean :10
## 3rd Qu.:10
## Max. :10
summary(sim_Afix50)
## machoid dcach foot freq
## Length:50000 Min. : 0.0 Min. : 0.000 Min. :4852
## Class :character 1st Qu.:12.0 1st Qu.: 0.000 1st Qu.:5564
## Mode :character Median :24.5 Median : 0.000 Median :5700
## Mean :24.5 Mean : 2.107 Mean :5700
## 3rd Qu.:37.0 3rd Qu.: 4.000 3rd Qu.:5834
## Max. :49.0 Max. :22.000 Max. :6621
## tama footpad freqpad tamapad
## Min. :32.68 Min. :-0.7003 Min. :-3.671140 Min. :-4.145233
## 1st Qu.:39.04 1st Qu.:-0.6147 1st Qu.:-0.682248 1st Qu.:-0.677661
## Median :40.40 Median :-0.5822 Median :-0.001761 Median :-0.003177
## Mean :40.39 Mean : 0.0000 Mean : 0.000000 Mean : 0.000000
## 3rd Qu.:41.74 3rd Qu.: 0.4174 3rd Qu.: 0.673657 3rd Qu.: 0.677619
## Max. :48.44 Max. : 4.8565 Max. : 3.944301 Max. : 3.900995
## exprlin prob distf ttot
## Min. :-5.28807 Min. :0.005026 Min. : 1.00 Min. : 1.0
## 1st Qu.:-0.95659 1st Qu.:0.277562 1st Qu.:16.40 1st Qu.: 341.4
## Median :-0.06129 Median :0.484682 Median :25.63 Median : 670.0
## Mean : 0.00000 Mean :0.494654 Mean :26.11 Mean : 670.4
## 3rd Qu.: 0.88134 3rd Qu.:0.707099 3rd Qu.:35.23 3rd Qu.: 995.3
## Max. : 6.04080 Max. :0.997626 Max. :65.76 Max. :1541.4
## nsim femea area femeasim
## Length:50000 Length:50000 Min. :50 Length:50000
## Class :character Class :character 1st Qu.:50 Class :character
## Mode :character Mode :character Median :50 Mode :character
## Mean :50
## 3rd Qu.:50
## Max. :50
summary(sim_Afix100) #arrumar dps pra rodar
## machoid dcach foot freq
## Length:100000 Min. : 0.00 Min. : 0.000 Min. :4718
## Class :character 1st Qu.:24.75 1st Qu.: 0.000 1st Qu.:5565
## Mode :character Median :49.50 Median : 0.000 Median :5701
## Mean :49.50 Mean : 1.053 Mean :5700
## 3rd Qu.:74.25 3rd Qu.: 0.000 3rd Qu.:5837
## Max. :99.00 Max. :21.000 Max. :6837
## tama footpad freqpad tamapad
## Min. :31.70 Min. :-0.4417 Min. :-4.915929 Min. :-3.924955
## 1st Qu.:39.06 1st Qu.:-0.4022 1st Qu.:-0.670649 1st Qu.:-0.675504
## Median :40.42 Median :-0.3896 Median :-0.000123 Median : 0.002585
## Mean :40.41 Mean : 0.0000 Mean : 0.000000 Mean : 0.000000
## 3rd Qu.:41.76 3rd Qu.:-0.3692 3rd Qu.: 0.678320 3rd Qu.: 0.675508
## Max. :49.25 Max. : 6.8602 Max. : 5.281986 Max. : 3.988209
## exprlin prob distf ttot
## Min. :-5.5160 Min. :0.004006 Min. : 1.00 Min. : 1.414
## 1st Qu.:-0.9411 1st Qu.:0.280677 1st Qu.: 32.89 1st Qu.:1343.041
## Median :-0.0930 Median :0.476766 Median : 51.09 Median :2657.469
## Mean : 0.0000 Mean :0.491412 Mean : 52.16 Mean :2653.933
## 3rd Qu.: 0.8113 3rd Qu.:0.692384 3rd Qu.: 70.46 3rd Qu.:3960.082
## Max. : 7.3049 Max. :0.999328 Max. :135.15 Max. :5979.006
## nsim femea area femeasim
## Length:100000 Length:100000 Min. :100 Length:100000
## Class :character Class :character 1st Qu.:100 Class :character
## Mode :character Mode :character Median :100 Mode :character
## Mean :100
## 3rd Qu.:100
## Max. :100
Optamos pelo uso de modelos generalizados mistos, pois pode haver um
efeito aleatório de cada rio (a variação entre rios pode ser maior do
que a variação dentro de um mesmo rio). Além disso, optamos por utilizar
a distribuição Gama, pois estamos interessados no tempo até a fêmea
escolher um macho e iniciar o amplexo. A distribuição Gamma é uma
gereralização da distribuição exponencial e é uma boa opção para modelar
o tempo até N eventos ocorrerem. Esta distribuição possui dois
parâmetros: shape (k) e scale (\(\theta\)). Como nossa variável é o tempo
até um determinado macho atingir amplexo, a distribuição Gammma é
apropriada. É frequente que os GLMM Gamma sejam difícies de implementar,
especialmente utilizando a função de ligação canônica
“inverse” (Bolker at al 2022). Por esse motivo, alguns
autores, como Lo e Andrews (2015) indicam utiliar a função de ligação
“log”, a qual utilizaremos aqui.
Os seguintes pacotes foram utilizados para as análises estatísticas e plotagem:
library(AICcmodavg) # Model Selection and Multimodel Inference Based on (Q)AIC(c)
library(ggplot2) # Create Elegant Data Visualisations Using the Grammar of Graphics
library(gridExtra) # Miscellaneous Functions for "Grid" Graphics
library(lme4) # Linear Mixed-Effects Models using 'Eigen' and S4
library(MASS) # Support Functions and Datasets for Venables and Ripley's MASS
library(bbmle) # Tools for General Maximum Likelihood Estimation
library(interactions) # Comprehensive, User-Friendly Toolkit for Probing Interactions
library(tibble) # Simple Data Frames
library(tidyverse) # Easily Install and Load the 'Tidyverse'
library(broom) # Convert Statistical Objects into Tidy Tibbles
library(multcomp) # Simultaneous Inference in General Parametric Models
AED(sim_Afix10, binw = 3)
# 1. GLMM Cheio: efeito aleatório das cachoeiras sobre o intercepto + efeito fixo com tripla interação
glmm10.1 = glmer(ttot~tamapad*freqpad*footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix10)
# 2. GLMM sem tripla
glmm10.2 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad+tamapad:footpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix10)
# 3. GLMM sem 1 dupla: freqpad:footpad
glmm10.3 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad+tamapad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix10)
# 4. GLMM sem 1 dupla: tamapad:footpad
glmm10.4 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix10)
# 5. GLMM sem 1 dupla: tamapad:freqpad
glmm10.5 = glmer(ttot~tamapad+freqpad+footpad+tamapad:footpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix10)
# 6. GLMM sem 2 duplas: freqpad:footpad e tamapad:footpad
glmm10.6 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix10)
# 7. GLMM sem 2 duplas: tamapad:footpad e tamapad:freqpad
glmm10.7 = glmer(ttot~tamapad+freqpad+footpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix10)
# 8. GLMM sem 2 duplas: freqpad:footpad e tamapad:freqpad
glmm10.8 = glmer(ttot~tamapad+freqpad+footpad+tamapad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix10)
# 9. GLMM sem nenhuma dupla
glmm10.9 = glmer(ttot~tamapad+freqpad+footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix10)
# 10. GLMM sem freqpad
glmm10.10 = glmer(ttot~tamapad+footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix10)
# 11. GLMM sem footpad
glmm10.11 = glmer(ttot~tamapad+freqpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix10)
# 12. GLMM sem tamapad
glmm10.12 = glmer(ttot~freqpad+footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix10)
# 13. GLMM só com freqpad
glmm10.13 = glmer(ttot~freqpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix10)
# 14. GLMM só com footpad
glmm10.14 = glmer(ttot~footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix10)
# 15. GLMM só com tamapad
glmm10.15 = glmer(ttot~tamapad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix10)
# Seleção do Modelo
models10 = c(glmm10.1, glmm10.2, glmm10.3, glmm10.4, glmm10.5, glmm10.6, glmm10.7, glmm10.8, glmm10.9, glmm10.10, glmm10.11, glmm10.12, glmm10.13, glmm10.14, glmm10.15)
model.names10 = c("glmm10.1", "glmm10.2", "glmm10.3", "glmm10.4", "glmm10.5", "glmm10.6", "glmm10.7", "glmm10.8", "glmm10.9", "glmm10.10", "glmm10.11", "glmm10.12", "glmm10.13", "glmm10.14", "glmm10.15")
aictab(cand.set=models10, modnames=model.names10, refit=FALSE)
##
## Model selection based on AICc:
##
## K AICc Delta_AICc AICcWt Cum.Wt LL
## glmm10.4 8 82671.18 0.00 0.45 0.45 -41327.58
## glmm10.2 9 82672.94 1.76 0.19 0.64 -41327.46
## glmm10.1 10 82673.18 2.00 0.17 0.81 -41326.58
## glmm10.7 7 82673.97 2.79 0.11 0.92 -41329.98
## glmm10.5 8 82675.71 4.53 0.05 0.96 -41329.85
## glmm10.6 7 82677.51 6.33 0.02 0.98 -41331.75
## glmm10.3 8 82679.29 8.11 0.01 0.99 -41331.64
## glmm10.9 6 82679.73 8.55 0.01 1.00 -41333.86
## glmm10.8 7 82681.53 10.35 0.00 1.00 -41333.76
## glmm10.12 5 82883.70 212.52 0.00 1.00 -41436.85
## glmm10.11 5 83154.00 482.82 0.00 1.00 -41572.00
## glmm10.13 4 83326.35 655.17 0.00 1.00 -41659.17
## glmm10.10 5 83515.84 844.66 0.00 1.00 -41752.92
## glmm10.14 4 83716.64 1045.46 0.00 1.00 -41854.32
## glmm10.15 4 83974.54 1303.36 0.00 1.00 -41983.27
# Sumário do melhor modelo
summary(glmm10.1)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Gamma ( log )
## Formula: ttot ~ tamapad * freqpad * footpad + (1 | nsim)
## Data: sim_Afix10
##
## AIC BIC logLik deviance df.resid
## 82673.2 82745.3 -41326.6 82653.2 9990
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8574 -0.7849 0.0173 0.7050 4.1392
##
## Random effects:
## Groups Name Variance Std.Dev.
## nsim (Intercept) 0.003937 0.06274
## Residual 0.274548 0.52397
## Number of obs: 10000, groups: nsim, 1000
##
## Fixed effects:
## Estimate Std. Error t value Pr(>|z|)
## (Intercept) 3.335546 0.006877 485.016 < 2e-16 ***
## tamapad -0.092918 0.006416 -14.483 < 2e-16 ***
## freqpad 0.188586 0.006368 29.614 < 2e-16 ***
## footpad -0.142787 0.006393 -22.335 < 2e-16 ***
## tamapad:freqpad -0.014930 0.006827 -2.187 0.02875 *
## tamapad:footpad -0.003438 0.006733 -0.511 0.60960
## freqpad:footpad -0.019689 0.006750 -2.917 0.00353 **
## tamapad:freqpad:footpad -0.009425 0.007092 -1.329 0.18387
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) tamapd freqpd footpd tmpd:fr tmpd:ft frqpd:
## tamapad 0.005
## freqpad -0.007 0.006
## footpad 0.009 0.036 0.006
## tampd:frqpd 0.010 0.016 -0.007 0.000
## tamapd:ftpd 0.023 0.003 0.000 0.024 -0.007
## freqpd:ftpd 0.012 0.000 -0.020 0.025 0.044 0.006
## tmpd:frqpd: 0.004 -0.005 0.044 0.009 -0.001 0.014 0.021
summary(glmm10.2)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Gamma ( log )
## Formula:
## ttot ~ tamapad + freqpad + footpad + tamapad:freqpad + tamapad:footpad +
## freqpad:footpad + (1 | nsim)
## Data: sim_Afix10
##
## AIC BIC logLik deviance df.resid
## 82672.9 82737.8 -41327.5 82654.9 9991
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8568 -0.7843 0.0144 0.7068 3.9575
##
## Random effects:
## Groups Name Variance Std.Dev.
## nsim (Intercept) 0.003897 0.06242
## Residual 0.274600 0.52402
## Number of obs: 10000, groups: nsim, 1000
##
## Fixed effects:
## Estimate Std. Error t value Pr(>|z|)
## (Intercept) 3.335610 0.006871 485.433 < 2e-16 ***
## tamapad -0.092961 0.006417 -14.487 < 2e-16 ***
## freqpad 0.188952 0.006364 29.692 < 2e-16 ***
## footpad -0.142702 0.006393 -22.321 < 2e-16 ***
## tamapad:freqpad -0.014925 0.006830 -2.185 0.02887 *
## tamapad:footpad -0.003323 0.006732 -0.494 0.62159
## freqpad:footpad -0.019504 0.006750 -2.890 0.00386 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) tamapd freqpd footpd tmpd:fr tmpd:ft
## tamapad 0.005
## freqpad -0.007 0.006
## footpad 0.009 0.037 0.005
## tampd:frqpd 0.010 0.016 -0.007 0.007
## tamapd:ftpd 0.023 0.003 0.007 0.024 -0.008
## freqpd:ftpd 0.012 0.008 -0.021 0.024 0.044 0.007
summary(glmm10.3)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Gamma ( log )
## Formula:
## ttot ~ tamapad + freqpad + footpad + tamapad:freqpad + tamapad:footpad +
## (1 | nsim)
## Data: sim_Afix10
##
## AIC BIC logLik deviance df.resid
## 82679.3 82737.0 -41331.6 82663.3 9992
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8544 -0.7849 0.0218 0.7016 4.3226
##
## Random effects:
## Groups Name Variance Std.Dev.
## nsim (Intercept) 0.003824 0.06184
## Residual 0.275044 0.52445
## Number of obs: 10000, groups: nsim, 1000
##
## Fixed effects:
## Estimate Std. Error t value Pr(>|z|)
## (Intercept) 3.335984 0.006861 486.214 <2e-16 ***
## tamapad -0.092821 0.006420 -14.458 <2e-16 ***
## freqpad 0.188573 0.006367 29.619 <2e-16 ***
## footpad -0.142212 0.006394 -22.241 <2e-16 ***
## tamapad:freqpad -0.014056 0.006826 -2.059 0.0395 *
## tamapad:footpad -0.003178 0.006731 -0.472 0.6368
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) tamapd freqpd footpd tmpd:fr
## tamapad 0.005
## freqpad -0.007 0.006
## footpad 0.009 0.037 0.023
## tampd:frqpd 0.010 0.015 -0.005 0.006
## tamapd:ftpd 0.023 0.003 0.007 0.023 0.009
summary(glmm10.4)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Gamma ( log )
## Formula:
## ttot ~ tamapad + freqpad + footpad + tamapad:freqpad + freqpad:footpad +
## (1 | nsim)
## Data: sim_Afix10
##
## AIC BIC logLik deviance df.resid
## 82671.2 82728.8 -41327.6 82655.2 9992
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8567 -0.7845 0.0137 0.7064 3.9783
##
## Random effects:
## Groups Name Variance Std.Dev.
## nsim (Intercept) 0.003922 0.06263
## Residual 0.274608 0.52403
## Number of obs: 10000, groups: nsim, 1000
##
## Fixed effects:
## Estimate Std. Error t value Pr(>|z|)
## (Intercept) 3.335692 0.006874 485.288 < 2e-16 ***
## tamapad -0.092951 0.006417 -14.486 < 2e-16 ***
## freqpad 0.188975 0.006363 29.697 < 2e-16 ***
## footpad -0.142627 0.006392 -22.315 < 2e-16 ***
## tamapad:freqpad -0.014952 0.006830 -2.189 0.02858 *
## freqpad:footpad -0.019477 0.006750 -2.886 0.00391 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) tamapd freqpd footpd tmpd:f
## tamapad 0.005
## freqpad -0.007 0.006
## footpad 0.008 0.040 0.005
## tampd:frqpd 0.010 0.016 -0.007 0.008
## freqpd:ftpd 0.012 0.008 -0.021 0.024 0.047
summary(glmm10.5)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Gamma ( log )
## Formula:
## ttot ~ tamapad + freqpad + footpad + tamapad:footpad + freqpad:footpad +
## (1 | nsim)
## Data: sim_Afix10
##
## AIC BIC logLik deviance df.resid
## 82675.7 82733.4 -41329.8 82659.7 9992
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8571 -0.7871 0.0197 0.7033 4.0070
##
## Random effects:
## Groups Name Variance Std.Dev.
## nsim (Intercept) 0.003857 0.0621
## Residual 0.274787 0.5242
## Number of obs: 10000, groups: nsim, 1000
##
## Fixed effects:
## Estimate Std. Error t value Pr(>|z|)
## (Intercept) 3.335831 0.006866 485.844 < 2e-16 ***
## tamapad -0.092736 0.006418 -14.450 < 2e-16 ***
## freqpad 0.188856 0.006367 29.664 < 2e-16 ***
## footpad -0.142601 0.006394 -22.301 < 2e-16 ***
## tamapad:footpad -0.003437 0.006734 -0.510 0.60977
## freqpad:footpad -0.018857 0.006747 -2.795 0.00519 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) tamapd freqpd footpd tmpd:f
## tamapad 0.005
## freqpad -0.007 0.019
## footpad 0.009 0.037 0.006
## tamapd:ftpd 0.023 0.003 0.007 0.024
## freqpd:ftpd 0.012 0.007 -0.020 0.024 0.020
summary(glmm10.6)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Gamma ( log )
## Formula: ttot ~ tamapad + freqpad + footpad + tamapad:freqpad + (1 | nsim)
## Data: sim_Afix10
##
## AIC BIC logLik deviance df.resid
## 82677.5 82728.0 -41331.7 82663.5 9993
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8543 -0.7852 0.0218 0.7003 4.3678
##
## Random effects:
## Groups Name Variance Std.Dev.
## nsim (Intercept) 0.003849 0.06204
## Residual 0.275051 0.52445
## Number of obs: 10000, groups: nsim, 1000
##
## Fixed effects:
## Estimate Std. Error t value Pr(>|z|)
## (Intercept) 3.336061 0.006863 486.078 <2e-16 ***
## tamapad -0.092812 0.006420 -14.457 <2e-16 ***
## freqpad 0.188595 0.006366 29.624 <2e-16 ***
## footpad -0.142141 0.006392 -22.236 <2e-16 ***
## tamapad:freqpad -0.014029 0.006825 -2.055 0.0398 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) tamapd freqpd footpd
## tamapad 0.005
## freqpad -0.007 0.006
## footpad 0.008 0.039 0.023
## tampd:frqpd 0.009 0.015 -0.006 0.006
summary(glmm10.7)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Gamma ( log )
## Formula: ttot ~ tamapad + freqpad + footpad + freqpad:footpad + (1 | nsim)
## Data: sim_Afix10
##
## AIC BIC logLik deviance df.resid
## 82674.0 82724.4 -41330.0 82660.0 9993
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8570 -0.7867 0.0187 0.7019 3.9933
##
## Random effects:
## Groups Name Variance Std.Dev.
## nsim (Intercept) 0.003883 0.06232
## Residual 0.274797 0.52421
## Number of obs: 10000, groups: nsim, 1000
##
## Fixed effects:
## Estimate Std. Error t value Pr(>|z|)
## (Intercept) 3.335917 0.006868 485.691 < 2e-16 ***
## tamapad -0.092726 0.006417 -14.449 < 2e-16 ***
## freqpad 0.188878 0.006366 29.669 < 2e-16 ***
## footpad -0.142522 0.006393 -22.294 < 2e-16 ***
## freqpad:footpad -0.018786 0.006745 -2.785 0.00535 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) tamapd freqpd footpd
## tamapad 0.005
## freqpad -0.007 0.019
## footpad 0.008 0.040 0.006
## freqpd:ftpd 0.011 0.007 -0.020 0.024
summary(glmm10.8)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Gamma ( log )
## Formula: ttot ~ tamapad + freqpad + footpad + tamapad:footpad + (1 | nsim)
## Data: sim_Afix10
##
## AIC BIC logLik deviance df.resid
## 82681.5 82732.0 -41333.8 82667.5 9993
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8548 -0.7888 0.0247 0.6964 4.2810
##
## Random effects:
## Groups Name Variance Std.Dev.
## nsim (Intercept) 0.003788 0.06155
## Residual 0.275205 0.52460
## Number of obs: 10000, groups: nsim, 1000
##
## Fixed effects:
## Estimate Std. Error t value Pr(>|z|)
## (Intercept) 3.336190 0.006856 486.595 <2e-16 ***
## tamapad -0.092618 0.006421 -14.425 <2e-16 ***
## freqpad 0.188499 0.006369 29.595 <2e-16 ***
## footpad -0.142129 0.006395 -22.224 <2e-16 ***
## tamapad:footpad -0.003063 0.006732 -0.455 0.649
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) tamapd freqpd footpd
## tamapad 0.005
## freqpad -0.007 0.019
## footpad 0.008 0.037 0.023
## tamapd:ftpd 0.023 0.003 0.007 0.023
summary(glmm10.9)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Gamma ( log )
## Formula: ttot ~ tamapad + freqpad + footpad + (1 | nsim)
## Data: sim_Afix10
##
## AIC BIC logLik deviance df.resid
## 82679.7 82723.0 -41333.9 82667.7 9994
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8547 -0.7867 0.0229 0.6965 4.2618
##
## Random effects:
## Groups Name Variance Std.Dev.
## nsim (Intercept) 0.003812 0.06174
## Residual 0.275210 0.52460
## Number of obs: 10000, groups: nsim, 1000
##
## Fixed effects:
## Estimate Std. Error t value Pr(>|z|)
## (Intercept) 3.336264 0.006858 486.47 <2e-16 ***
## tamapad -0.092608 0.006421 -14.42 <2e-16 ***
## freqpad 0.188521 0.006369 29.60 <2e-16 ***
## footpad -0.142061 0.006394 -22.22 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) tamapd freqpd
## tamapad 0.005
## freqpad -0.007 0.019
## footpad 0.008 0.040 0.023
plot_tendencia(dados = sim_Afix10, modelo = glmm10.9)
# Intervalo de confiança dos coeficientes das preditoras
conf10 = as.data.frame(confint(glmm10.1, method="Wald"))
conf10 = conf10[-(1:3),]
conf10$coef = glmm10.1@beta[-1]
conf10 = tibble::rownames_to_column(conf10, "Predictor")
colnames(conf10)[c(2,3)] = c("min25", "max975")
conf10
## Predictor min25 max975 coef
## 1 tamapad -0.10549245 -0.080343004 -0.092917728
## 2 freqpad 0.17610427 0.201066906 0.188585586
## 3 footpad -0.15531652 -0.130256610 -0.142786567
## 4 tamapad:freqpad -0.02831052 -0.001549196 -0.014929859
## 5 tamapad:footpad -0.01663386 0.009757871 -0.003437997
## 6 freqpad:footpad -0.03291805 -0.006459881 -0.019688965
## 7 tamapad:freqpad:footpad -0.02332430 0.004475254 -0.009424524
ggplot(conf10, aes(x=coef, y=Predictor)) +
geom_point() +
geom_errorbar(aes(xmin=min25, xmax=max975), width=0.3)+
xlab("\nIntervalos de confiança (95%)")+
geom_vline(xintercept=0, colour="red")
AED(sim_Afix50, binw = 70)
# 1. GLMM Cheio: efeito aleatório das cachoeiras sobre o intercepto + efeito fixo com tripla interação
glmm50.1 = glmer(ttot~tamapad*freqpad*footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix50)
# 2. GLMM sem tripla
glmm50.2 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad+tamapad:footpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix50)
# 3. GLMM sem 1 dupla: freqpad:footpad
glmm50.3 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad+tamapad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix50)
# 4. GLMM sem 1 dupla: tamapad:footpad
glmm50.4 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix50)
# 5. GLMM sem 1 dupla: tamapad:freqpad
glmm50.5 = glmer(ttot~tamapad+freqpad+footpad+tamapad:footpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix50)
# 6. GLMM sem 2 duplas: freqpad:footpad e tamapad:footpad
glmm50.6 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix50)
# 7. GLMM sem 2 duplas: tamapad:footpad e tamapad:freqpad
glmm50.7 = glmer(ttot~tamapad+freqpad+footpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix50)
# 8. GLMM sem 2 duplas: freqpad:footpad e tamapad:freqpad
glmm50.8 = glmer(ttot~tamapad+freqpad+footpad+tamapad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix50)
# 9. GLMM sem nenhuma dupla
glmm50.9 = glmer(ttot~tamapad+freqpad+footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix50)
# 10. GLMM sem freqpad
glmm50.10 = glmer(ttot~tamapad+footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix50)
# 11. GLMM sem footpad
glmm50.11 = glmer(ttot~tamapad+freqpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix50)
# 12. GLMM sem tamapad
glmm50.12 = glmer(ttot~freqpad+footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix50)
# 13. GLMM só com freqpad
glmm50.13 = glmer(ttot~freqpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix50)
# 14. GLMM só com footpad
glmm50.14 = glmer(ttot~footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix50)
# 15. GLMM só com tamapad
glmm50.15 = glmer(ttot~tamapad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix50)
# Seleção de modelo
models50 = c(glmm50.1, glmm50.2, glmm50.3, glmm50.4, glmm50.5, glmm50.6, glmm50.7, glmm50.8, glmm50.9, glmm50.10, glmm50.11, glmm50.12, glmm50.13, glmm50.14, glmm50.15)
model.names50 = gsub("10", "50", model.names10)
aictab(cand.set=models50, modnames=model.names50)
##
## Model selection based on AICc:
##
## K AICc Delta_AICc AICcWt Cum.Wt LL
## glmm50.1 10 732883.5 0.00 0.93 0.93 -366431.8
## glmm50.2 9 732888.7 5.14 0.07 1.00 -366435.3
## glmm50.4 8 732905.1 21.56 0.00 1.00 -366444.5
## glmm50.5 8 732910.1 26.53 0.00 1.00 -366447.0
## glmm50.7 7 732926.3 42.74 0.00 1.00 -366456.1
## glmm50.3 8 733040.1 156.59 0.00 1.00 -366512.0
## glmm50.8 7 733053.9 170.42 0.00 1.00 -366520.0
## glmm50.6 7 733055.9 172.38 0.00 1.00 -366521.0
## glmm50.9 6 733070.8 187.31 0.00 1.00 -366529.4
## glmm50.12 5 734046.8 1163.32 0.00 1.00 -367018.4
## glmm50.11 5 734861.0 1977.47 0.00 1.00 -367425.5
## glmm50.13 4 735712.2 2828.69 0.00 1.00 -367852.1
## glmm50.50 5 737492.8 4609.24 0.00 1.00 -368741.4
## glmm50.14 4 738422.1 5538.54 0.00 1.00 -369207.0
## glmm50.15 4 739364.0 6480.50 0.00 1.00 -369678.0
# Sumário do melhor modelo
summary(glmm50.1)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Gamma ( log )
## Formula: ttot ~ tamapad * freqpad * footpad + (1 | nsim)
## Data: sim_Afix50
##
## AIC BIC logLik deviance df.resid
## 732883.5 732971.7 -366431.8 732863.5 49990
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8507 -0.7937 0.0538 0.7161 4.6086
##
## Random effects:
## Groups Name Variance Std.Dev.
## nsim (Intercept) 0.0002167 0.01472
## Residual 0.2911624 0.53959
## Number of obs: 50000, groups: nsim, 1000
##
## Fixed effects:
## Estimate Std. Error t value Pr(>|z|)
## (Intercept) 6.472961 0.003108 2082.988 < 2e-16 ***
## tamapad -0.095467 0.003024 -31.569 < 2e-16 ***
## freqpad 0.204662 0.003006 68.086 < 2e-16 ***
## footpad -0.134091 0.003021 -44.394 < 2e-16 ***
## tamapad:freqpad -0.014468 0.003031 -4.773 1.82e-06 ***
## tamapad:footpad 0.012929 0.003032 4.264 2.01e-05 ***
## freqpad:footpad -0.037108 0.002956 -12.555 < 2e-16 ***
## tamapad:freqpad:footpad -0.007953 0.002976 -2.672 0.00754 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) tamapd freqpd footpd tmpd:fr tmpd:ft frqpd:
## tamapad 0.001
## freqpad -0.002 -0.005
## footpad 0.005 0.053 0.005
## tampd:frqpd -0.003 0.005 -0.026 -0.001
## tamapd:ftpd 0.050 0.002 0.000 0.069 -0.005
## freqpd:ftpd 0.006 -0.001 -0.020 0.007 0.068 -0.018
## tmpd:frqpd: 0.000 -0.004 0.067 -0.018 -0.023 0.012 0.070
# Intervalo de confiança dos coeficientes das preditoras
# conf10.1 = confint(glmm10.1, method="Wald")
plot_tendencia(dados = sim_Afix50, modelo = glmm50.1)
AED(sim_Afix100, binw = 200)
# 1. GLMM Cheio: efeito aleatório das cachoeiras sobre o intercepto + efeito fixo com tripla interação
glmm100.1 = glmer(ttot~tamapad*freqpad*footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix100)
# 2. GLMM sem tripla
glmm100.2 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad+tamapad:footpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix100)
# 3. GLMM sem 1 dupla: freqpad:footpad
glmm100.3 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad+tamapad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix100)
# 4. GLMM sem 1 dupla: tamapad:footpad
glmm100.4 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix100)
# 5. GLMM sem 1 dupla: tamapad:freqpad
glmm100.5 = glmer(ttot~tamapad+freqpad+footpad+tamapad:footpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix100)
# 6. GLMM sem 2 duplas: freqpad:footpad e tamapad:footpad
glmm100.6 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix100)
# 7. GLMM sem 2 duplas: tamapad:footpad e tamapad:freqpad
glmm100.7 = glmer(ttot~tamapad+freqpad+footpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix100)
# 8. GLMM sem 2 duplas: freqpad:footpad e tamapad:freqpad
glmm100.8 = glmer(ttot~tamapad+freqpad+footpad+tamapad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix100)
# 9. GLMM sem nenhuma dupla
glmm100.9 = glmer(ttot~tamapad+freqpad+footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix100)
# 10. GLMM sem freqpad
glmm100.10 = glmer(ttot~tamapad+footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix100)
# 11. GLMM sem footpad
glmm100.11 = glmer(ttot~tamapad+freqpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix100)
# 12. GLMM sem tamapad
glmm100.12 = glmer(ttot~freqpad+footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix100)
# 13. GLMM só com freqpad
glmm100.13 = glmer(ttot~freqpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix100)
# 14. GLMM só com footpad
glmm100.14 = glmer(ttot~footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix100)
# 15. GLMM só com tamapad
glmm100.15 = glmer(ttot~tamapad + (1|nsim), family=Gamma(link = "log"), data=sim_Afix100)
# Seleção de modelo
models100 = c(glmm100.1, glmm100.2, glmm100.3, glmm100.4, glmm100.5, glmm100.6, glmm100.7, glmm100.8, glmm100.9, glmm100.10, glmm100.11, glmm100.12, glmm100.13, glmm100.14, glmm100.15)
model.names100 = gsub("10", "100", model.names10)
aictab(cand.set=models100, modnames=model.names100)
##
## Model selection based on AICc:
##
## K AICc Delta_AICc AICcWt Cum.Wt LL
## glmm100.2 9 1743713 0.00 0.61 0.61 -871847.5
## glmm100.1 10 1743714 0.86 0.39 1.00 -871846.9
## glmm100.5 8 1743782 68.57 0.00 1.00 -871882.8
## glmm100.4 8 1743796 82.60 0.00 1.00 -871889.8
## glmm100.7 7 1743863 150.31 0.00 1.00 -871924.7
## glmm100.3 8 1744174 460.84 0.00 1.00 -872078.9
## glmm100.8 7 1744223 510.05 0.00 1.00 -872104.5
## glmm100.6 7 1744262 549.05 0.00 1.00 -872124.0
## glmm100.9 6 1744317 603.88 0.00 1.00 -872152.4
## glmm100.12 5 1746192 2478.58 0.00 1.00 -873090.8
## glmm100.11 5 1746640 2927.00 0.00 1.00 -873315.0
## glmm100.13 4 1748402 4689.30 0.00 1.00 -874197.2
## glmm100.100 5 1753041 9327.95 0.00 1.00 -876515.5
## glmm100.14 4 1754889 11176.26 0.00 1.00 -877440.6
## glmm100.15 4 1755633 11920.43 0.00 1.00 -877812.7
# Sumário do melhor modelo
summary(glmm100.1)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Gamma ( log )
## Formula: ttot ~ tamapad * freqpad * footpad + (1 | nsim)
## Data: sim_Afix100
##
## AIC BIC logLik deviance df.resid
## 1743713.9 1743809.0 -871846.9 1743693.9 99990
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8436 -0.8071 0.0640 0.7294 5.2627
##
## Random effects:
## Groups Name Variance Std.Dev.
## nsim (Intercept) 0.0000 0.0000
## Residual 0.2938 0.5421
## Number of obs: 100000, groups: nsim, 1000
##
## Fixed effects:
## Estimate Std. Error t value Pr(>|z|)
## (Intercept) 7.850223 0.002169 3618.843 <2e-16 ***
## tamapad -0.095468 0.002175 -43.887 <2e-16 ***
## freqpad 0.206544 0.002153 95.923 <2e-16 ***
## footpad -0.112533 0.002157 -52.164 <2e-16 ***
## tamapad:freqpad -0.018058 0.002152 -8.392 <2e-16 ***
## tamapad:footpad 0.019634 0.002128 9.225 <2e-16 ***
## freqpad:footpad -0.045886 0.002132 -21.518 <2e-16 ***
## tamapad:freqpad:footpad -0.002260 0.002113 -1.070 0.285
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) tamapd freqpd footpd tmpd:fr tmpd:ft frqpd:
## tamapad 0.000
## freqpad 0.001 -0.002
## footpad 0.003 0.039 0.008
## tampd:frqpd -0.001 -0.001 -0.021 0.008
## tamapd:ftpd 0.039 -0.008 0.007 0.084 -0.005
## freqpd:ftpd 0.009 0.008 -0.003 0.014 0.055 0.007
## tmpd:frqpd: 0.008 -0.004 0.055 0.008 -0.009 -0.023 0.104
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
# Intervalo de confiança dos coeficientes das preditoras
# conf10.1 = confint(glmm10.1, method="Wald")
plot_tendencia(dados = sim_Afix100, modelo = glmm100.1)
# Padroniza área
sim_Avar$areapad = padroniza(sim_Avar$area)
# AED
AED(sim_Avar, binw = 200)
# GLMM cheio com área
glmmvar.1area = glmer(ttot~tamapad*freqpad*footpad*I(areapad^2) + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# GLMM apenas triplas
glmmvar.2area = glmer(ttot~tamapad+freqpad+footpad+ I(area^2)+tamapad:freqpad+tamapad:footpad+freqpad:footpad+I(area^2):tamapad+I(area^2):freqpad+I(area^2):footpad+tamapad:freqpad:footpad+tamapad:freqpad:footpad:I(area^2) + (1|nsim), family)
# 1. GLMM Cheio: efeito aleatório das cachoeiras sobre o intercepto + efeito fixo com tripla interação
glmmvar.1 = glmer(ttot~tamapad*freqpad*footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# 2. GLMM sem tripla
glmmvar.2 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad+tamapad:footpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# 3. GLMM sem 1 dupla: freqpad:footpad
glmmvar.3 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad+tamapad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# 4. GLMM sem 1 dupla: tamapad:footpad
glmmvar.4 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# 5. GLMM sem 1 dupla: tamapad:freqpad
glmmvar.5 = glmer(ttot~tamapad+freqpad+footpad+tamapad:footpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# 6. GLMM sem 2 duplas: freqpad:footpad e tamapad:footpad
glmmvar.6 = glmer(ttot~tamapad+freqpad+footpad+tamapad:freqpad + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# 7. GLMM sem 2 duplas: tamapad:footpad e tamapad:freqpad
glmmvar.7 = glmer(ttot~tamapad+freqpad+footpad+freqpad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# 8. GLMM sem 2 duplas: freqpad:footpad e tamapad:freqpad
glmmvar.8 = glmer(ttot~tamapad+freqpad+footpad+tamapad:footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# 9. GLMM sem nenhuma dupla
glmmvar.9 = glmer(ttot~tamapad+freqpad+footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# 10. GLMM sem freqpad
glmmvar.10 = glmer(ttot~tamapad+footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# 11. GLMM sem footpad
glmmvar.11 = glmer(ttot~tamapad+freqpad + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# 12. GLMM sem tamapad
glmmvar.12 = glmer(ttot~freqpad+footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# 13. GLMM só com freqpad
glmmvar.13 = glmer(ttot~freqpad + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# 14. GLMM só com footpad
glmmvar.14 = glmer(ttot~footpad + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# 15. GLMM só com tamapad
glmmvar.15 = glmer(ttot~tamapad + (1|nsim), family=Gamma(link = "log"), data=sim_Avar)
# Seleção de modelo
modelsvar = c(glmmvar.1, glmmvar.2, glmmvar.3, glmmvar.4, glmmvar.5, glmmvar.6, glmmvar.7, glmmvar.8, glmmvar.9, glmmvar.10, glmmvar.11, glmmvar.12, glmmvar.13, glmmvar.14, glmmvar.15)
model.namesvar = gsub("10", "var", model.names10)
aictab(cand.set=modelsvar, modnames=model.namesvar)
#summary(glmmvar.1)
#plot_tendencia(dados = sim_Avar, modelo = glmmvar.1)
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